Dietary recommendations have fluctuated widely for decades, and still differ substantially between sources. So far there is zero direct evidence that meat consumption causes fatty liver disease; I mean it's possible but we just don't know one way or the other. The only real data we have comes from low-quality observational studies (basically junk science).
If someone wants to try limiting meat consumption as an "n=1" experiment to see how it affects their body composition and other biomarkers then go ahead. Just don't expect a major impact from that one factor.
Generally speaking, I actually don't think I recall much of a link between meat and fatty liver, it always seemed to be closer linked to highly refined sugars and possibly high levels of dairy but less of a link there.
If someone wants to try limiting meat consumption as an "n=1" experiment to see how it affects their body composition and other biomarkers then go ahead. Just don't expect a major impact from that one factor.